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What is the equation for energy of a free electron as a function of wave vector k? Does electron momentum increase or decrease with k?
E=h_2k2/2m because E=1/2(mv2) and p=h_k
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Explain the T5 dependence of the conductivity of metals at temperatures well below the Debye temp.
p. 131 and p. 345, the conductivity is proportional to 1 over T5
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What is the Debye temperature?
The temperature above which all vibrational frequencies are executed by the lattice waves.
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Why is there a maximum cutoff frequency for phonons?
The wavelength cannot be shorter than a single unit cell.
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Does the Debye temperature increase with increased eleastic modulus, why?
Yes, seperation between states increases hence the need for more to fill them due to the elastic modulus.
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According to the Drude Model would you expect a stronger temperature dependence of conductivity (i.e. slope of conductivity vs T) with increased atom bond strength?
No, p is proportional to T/Omega2
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What is the fundamental equation of Electronic Materials?
sigma=(e)(n)(mu) where sigma=conductivity, e=electron charge, n=atoms/unit volume, and mu=electron mobility.
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Calculate the Fermi Energy (eV) of Cu=8.5x1028atoms/m3. The work function of Cu is 4.65 eV, draw a band diagram with relative positions of band bottom, Fermi Level, and vacuum level.
EFo=(h2/8me)(3n/pi)3/2, the bottom band (valence band) is located obviously at the bottom followed by the Fermi band with the fermi level located in the middle, and the vaccuum level (conduction band) located equally above the fermi level
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Calculate the drift mobilty and mean scatterin time of conduction electrons in Cu given a conductivity of 5.9x105 atoms/ohm(cm). Density of 8.96g/cm3, atomic mass=63.5g/mol, and 1 free electron/atom.
n=d(NA)/Mat) then mu=sigma/en=43.4 (cm2) then tau=(mu)me/e=2.5x10-14 s
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Does image charge effectively increase or reduce barrier height in emission process?
reduces p. 332 figure 4.36
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Understand E-K diagrams. What points are higher and lower energy, what are the directions within the crystal, and which points are closest in the real crystal?
Dependent on crystal and graph, higher point on graph have higher energy (graph is a fold over at the lines) and wikipedia has a good article on Brillouin Zones.
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Identify band gaps, heavy hole band, and difference between direct and indirect movementsin semiconductor band diagrams.
Heavy hole band is the highest band in the lower region before the band gap, the band gaps are the areas where know more vertical increments occur in the energy direction, indirect bandgaps occur when high point of the lower band and low point of the higher band do not align.
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How do you calculate the resistivity do to scattering?
p=1/en(mu)
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Does temperature effect the Fermi Level?
Yes, but the change in the Fermi level is negligible.
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What is the x-ray emission band and why is it referred to as the L-band?
The x-ray emission band is formed when an electron from a higher energy level falls down energy levels releasing a photon of x-ray emission. It is the L-band because it crosses into a Lower energy.
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What is the symbol for mean free path?
lowercase script L
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What is the symbol for conductivity?
sigma
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What is the symbol for drift mobility?
mu
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What is the symbol for density of states?
g(E)
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What is the symbol for Fermi Energy?
EFo
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What would test a material for semiconductor properties?
Measure the material's conductivity over a wide temperature range, the conductivity of a metal is not temperature activated.
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